Using Influence Lines for Uniformly Distributed Load Notes | EduRev

: Using Influence Lines for Uniformly Distributed Load Notes | EduRev

 Page 1


Module 6 : Influence Lines
Lecture 4 : Using Influence Lines for Uniformly Distributed Load
 Objectives
   In this course you will learn the following
How to use influence lines for distributed loading cases.
6.4 Using Influence Lines for Uniformly Distributed Load
 
Consider the simply-supported beam AB in Figure 6.5, of which the portion CD is acted upon by a uniformly
distributed load of intensity w/unit length . We want to find the value of a certain response function R
under this loading and let us assume that we have already constructed the influence line of this response
function. Let the ordinate of the influence line at a distance x from support A be . If we consider an
elemental length dx of the beam at a distance x from A , the total force acting on this elemental length is
wdx . Since dx is infinitesimal, we can consider this force to be a concentrated force acting at a distance x .
The contribution of this concentrated force wdx to R is:
                                       
 
Therefore, the total effect of the distributed force from point C to D is:
 
                               
 
                                (area under the influence line from C to D )
 
 Figure 6.5 Using influence line for a uniformly distributed loading
 
Thus, we can obtain the response parameter by multiplying the intensity of the uniformly distributed load
with the area under the influence line for the distance for which the load is acting. To illustrate, let us
consider the uniformly distributed load on a simply supported beam (Figure 6.6). To find the vertical
reaction at the left support, we can use the influence line for  that we have obtained in Example 6.1. So
we can calculate the reaction  as:
Page 2


Module 6 : Influence Lines
Lecture 4 : Using Influence Lines for Uniformly Distributed Load
 Objectives
   In this course you will learn the following
How to use influence lines for distributed loading cases.
6.4 Using Influence Lines for Uniformly Distributed Load
 
Consider the simply-supported beam AB in Figure 6.5, of which the portion CD is acted upon by a uniformly
distributed load of intensity w/unit length . We want to find the value of a certain response function R
under this loading and let us assume that we have already constructed the influence line of this response
function. Let the ordinate of the influence line at a distance x from support A be . If we consider an
elemental length dx of the beam at a distance x from A , the total force acting on this elemental length is
wdx . Since dx is infinitesimal, we can consider this force to be a concentrated force acting at a distance x .
The contribution of this concentrated force wdx to R is:
                                       
 
Therefore, the total effect of the distributed force from point C to D is:
 
                               
 
                                (area under the influence line from C to D )
 
 Figure 6.5 Using influence line for a uniformly distributed loading
 
Thus, we can obtain the response parameter by multiplying the intensity of the uniformly distributed load
with the area under the influence line for the distance for which the load is acting. To illustrate, let us
consider the uniformly distributed load on a simply supported beam (Figure 6.6). To find the vertical
reaction at the left support, we can use the influence line for  that we have obtained in Example 6.1. So
we can calculate the reaction  as:
                            
 
    
 
                                    Figure 6.6 Uniformly distributed load acting on a beam
 
Similarly, we can find any other response function for a uniformly distributed loading using their influence
lines as well.
For non-uniformly distributed loading, the intensity w is not constant through the length of the distributed
load. We can still use the integration formulation:
                           
 
However, we cannot take the intensity w outside the integral, as it is a function of x .
 Recap
   In this course you have learnt the following
How to use influence lines for distributed loading cases.
 
 
 
 
Read More
Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!